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Thermodynamic formalism for countable to one Markov systems
Author(s):
Michiko
Yuri
Journal:
Trans. Amer. Math. Soc.
355
(2003),
2949-2971.
MSC (2000):
Primary 28D99, 28D20, 58C40, 58E30, 37A40, 37A30, 37C30, 37D35, 37F10, 37A45
Posted:
March 19, 2003
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Abstract:
For countable to one transitive Markov systems we establish thermodynamic formalism for non-Hölder potentials in nonhyperbolic situations. We present a new method for the construction of conformal measures that satisfy the weak Gibbs property for potentials of weak bounded variation and show the existence of equilibrium states equivalent to the weak Gibbs measures. We see that certain periodic orbits cause a phase transition, non-Gibbsianness and force the decay of correlations to be slow. We apply our results to higher-dimensional maps with indifferent periodic points.
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Additional Information:
Michiko
Yuri
Affiliation:
Department of Business Administration, Sapporo University, Nishioka, Toyohira-ku, Sapporo 062-8520, Japan
Email:
yuri@math.sci.hokudai.ac.jp, yuri@mail-ext.sapporo-u.ac.jp
DOI:
10.1090/S0002-9947-03-03269-0
PII:
S 0002-9947(03)03269-0
Received by editor(s):
March 28, 2002
Received by editor(s) in revised form:
September 10, 2002
Posted:
March 19, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Michiko YURI, Multifractal Analysis of Weak Gibbs measures for Intermittent systems, Communications in Mathematical Physics 230 (2002), 365-388. (ENGLISH)
Michiko YURI, On the speed of convergence to equilibrium states for multi-dimensional maps wth indifferent periodic points, Nonlinearity 15 (2002), 429-445. (ENGLISH) MR 2002k:37006
Michiko YURI, Weak Gibbs measures and the local product structure, Ergodic Theory and Dynamical Systems 22 (2002), 1933-1955. (ENGLISH)
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